Dynamic mean-CVaR portfolio optimization in continuous-time

The conditional value-at-risk(CVaR) is defined as the expected value of the tail distribution exceeding Value-at-Risk(VaR). As a kind of risk measure, CVaR recently receives much attention from both academic field and financial industry. However, due to the tractability, most of the studies on mean-CVaR portfolio optimization are restricted to the static portfolio analysis, where only buy-and-hold portfolio policy is computed numerically. In this paper, we study the dynamic portfolio policy of the mean-CVaR portfolio model, in which the investor is allowed to adjust the investment policy dynamically to minimize the CVaR of the portfolio as well as keep certain level of the expected return. On recognizing the ill-posed nature of such a problem in continuous-time model, we modify the model by imposing the limited funding level as the upper bound of the wealth. By using the martingale approach, we develop the explicit portfolio policy and mean-CVaR efficient frontier for such a problem.